A ball striking device, such as a golf club head, includes a face having a ball striking surface configured for striking a ball and a body connected to the face and extending rearwardly from the face. The body has an impact-influencing structure in the form of a channel positioned on at least one surface of the body. A majority of a force generated by impact with a ball is absorbed by the impact-influencing structure, and a majority of a response force generated by the head upon impact with the ball is generated by the impact-influencing structure. The face may have increased stiffness as compared to existing faces, and may include a stiffening structure to create the increased stiffness, such as a porous or cellular stiffening structure.